Cots and beds using air mattresses to provide yieldable body supports are known in the art. For example, Young et al in U.S. Pat. No. 4,306,322 and Swenson et al in U.S. Pat. No. 4,394,784 disclose air bed assemblies having a pair of pneumatic bladders confined within an outer perimeter of four longitudinally extending foam rubber blocks. The air bladders and blocks are enclosed within a cover. These air bed assemblies do not have a border which uses top and bottom foam members of different density whereby the bottom member is sufficiently rigid to confine the air bladders within the perimeter of the border and the top member is sufficiently resilient to comfortably support a resting body.
Savenije in U.S. Pat. No. 4,682,378 discloses an air mattress assembly having edge strips of foam material extending around an air chamber. A top layer of foam material is secured to the edge strips to enclose the air chamber. The air bed of Savenije, however, suffers from the disadvantage that the resiliency and comfort of its edge strips is limited so as to sufficiently confine the air chamber within its perimeter.